Is proof essential to mathematics?
Despite the dominance of proof as the methodology of advanced mathematics courses, contemporary advances in applied, computer-aided, and so-called “experimental” mathematics have restored to mathematical practice much of the free-wheeling spirit of earlier eras. Indeed, these recent innovations have led some to proclaim the “death” of proofthat although proof is still useful in some contexts, it may no longer be the sine qua non of mathematical truth [Horgan, 1993]. Although this claim is hotly disputed by many leading mathematicians, it resonates with diverse pedagogical concerns about the appropriateness (or effectiveness) of proof as a tool for learning mathematics. Uncertainty about the role of proof in school mathematics caused NCTM in its Standards [NCTM, 1989] to resort to euphemisms”justify,” “validate,” “test conjectures,” “follow logical arguments.” Rarely do the Standards use the crystalline term “proof.” In fact, most people understand “proof” in a pragmatic rather than a p
